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The phrase "a weak influence on" is correct and usable in written English.
It can be used to describe a situation where something has a minimal or limited effect on another thing.
Example: "The study found that social media has a weak influence on the purchasing decisions of teenagers."
Alternatives: "a minor impact on" or "a slight effect on".
Exact(34)
Overall, the level of invasion has a weak influence on pollination network structure and seems to be associated with only one metric, H 2 ′ which measures the level of selectiveness; thus, as invasion progresses, species in the network appear to become more selective in their choice of partners, interacting with less abundant species more than would be expected by chance.
As the article notes, gas prices do seem to exert a weak influence on voting behavior.
Servo voltage has a weak influence on average wire amplitude.
Interface style and perceived ease of use had a weak influence on perceived enjoyment.
Polytypism has a weak influence on these results, especially regarding dislocation core energies and Peierls stress.
On the contrary, α value was found to have a weak influence on the Rs.
Similar(26)
Although linear regression did not show a significant influence of age on our findings, there was a weak influence of age on DCP in the control group.
There was also a stark contrast between genetic structure in the native range, which displayed a clear geographic cline from East to West, and in Europe, where we detected no pattern of isolation by distance and only a weak influence of geography on the genetic structure.
The results from Figure 6 show only a weak influence of the CFO on the STO estimation.
The stratospheric wind speeds along the great circle for each station suggest a weak influence of these winds on the signal periods (except for I04 AU).
Hence, the overall weak effect we found does not imply a weak influence of plant invasions on the reproductive success of native species.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com